I've been doing this periodically and his normal reaction is to slowly back away and hide. This last time, he backed away more slowly than I had ever seen him, and then became completely still, everything stopped moving except the occasional and barely visible movement from his pectoral fins. Almost like he was playing dead or thinking "if I don't move, they can't see me."
As soon as I moved the mirror away, he was fine.

On the other hand, I had to temporarily move my tanks very close to each other so I could set up his new one. He and my other fish could see each other. His initial reaction was to hide while she was flaring at him. Then he finally came out and started flaring, while she flared back and turned bright purple with dark vertical stripes and was she was swaying back and forth on her side with her head pointed down.

I have seen many reactions in fish from the mirror... Some investigate it, not scared at all... Another decided to attack the mirror repeatedly with his little mouth, some tail slap it, some circle it flaring, and others back away.

As for the female, take a look at the picture I have attached. This is Janey.. Once a pale little thing, now looks like she has been painted blue! Since breeding her (twice now) her color has enhanced and her caudal has gotten longer and fuller. It's a way of saying "I'm ready, and I'm viable to breed with you". The vertical stripes are submission stripes. I rarely get to see this anymore as I have mainly light girls but I have a few plakats who are darker that may be bred. That with the heads down slow and intent dance she was doing... Is saying "I submit fully to you".

He may have a different reaction seeing a male (the mirror) and seeing a female, as you noticed when he backed down to the mirror, but came out eventually to the female. He's a lover, not a fighter ;)

And contrare to popular belief, males don't right out attack each other (at least most of the time). They tend to put on a show... Circle each other, flare, chase, tail slap, stare down, etc, before actually harming each other. Though this is not true in some cases, most cases it is. It's a "I'm prettier than you, bigger than you, better than you."